Beliefs in Problem Solving: Case Study in Circles Tangents Line Materials

Abstract

The study aimed to reveal the belief profile of student' who had medium and low math ability in solving problems of circle tangent material. This type of research was qualitative research. Subject selection based on the ability of students, feedback from professors and fluency in communicating both verbally and writing. Data collection techniques used are the method of semi-structured interview with technique of think aloud method, students are asked to express clearly everything was thought out and asked to write directly. The results showed that subjects with high, medium and low mathematical ability: believed that the mathematical problems given have difficulty level of moderate and high. It was due to the subject does not have an initial picture of problems resolution, and there were several ways, and there were many stages to be solved. The time required in problem solving is about 20 minutes. Further subjects believed the concept of tangent is used to find the length of the chain that was not attached to the wheel, while the concept of the circumference was used to find the length of the chain attached to the wheel. The subject believed it could be completed in one way that is using the circumference of the circle and the external tangents. Subjects believed stages of problem solving begin by finding the circumference of a half circle for the big circle and half circle for a small circle. Next is finding the length of external tangents between circles. Although the subject believed the concept, relation between concepts, step-by-step solution; subjects are not sure of the answers that would be obtained from a solution that will be done. Finding in problem solving practices was the subject making the same mistake that is they could not represent the mathematical problems into mathematical images. This was due to all three subjects draw a diameter line on the big circle and a small circle thus when drawing a line connecting two points on each circle, the line was not tangent of both circles.